Find the value ofsin[2cot−1(12−5)]

Letcot−1(12−5)=y. Then coty=12−5Now sin[2cot−1(12−5)]=sin2y=2sinycosy=2(1312)(13−5)[since coty<0, so y∈(2π,π)]=196−120

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Find the value of [2^{-1}({-5}{12})]

Question

Find the value of
$sin [2 cot^{- 1} (\frac{- 5}{12})]$

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Samuel Discussed

Find the value of

sin [2 cot^{- 1} (\frac{- 5}{12})]

11 mins ago

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11 mins ago

Let

cot^{- 1} (\frac{- 5}{12}) = y

. Then

cot y = \frac{- 5}{12}

Now

sin [2 cot^{- 1} (\frac{- 5}{12})] = sin 2 y

= 2 sin y cos y = 2 (\frac{12}{13}) (\frac{- 5}{13}) [s in ce cot y < 0, so y \in (\frac{π}{2}, π)]

= \frac{- 120}{196}

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